Just heard back from the guy at the apartment-hunting service who showed me a few places on Friday and was going to show me a few more tonight. Found out that the "few more" for tonight would have only been one, and it was a garden level, which I'm not interested in, so no apartment-looking tonight.
Tomorrow night, there's an open house at the apartment I looked at on Friday that I liked (well, actually I looked at another 1BR in the same building, since the one that opens up on 5/1 was still occupado), so we're meeting there and I can get some queries I have about the place answered. It's about $25/mo more than I would have liked, but it's on the first floor up the stairs, is plenty big enough for most of my stuff, has a nice big new kitchen, and has a washer and dryer at the bottom of the back stairs (no more having to walk down the alleyway to get my clothes clean). Also, if I come into some extra cash, there is reserved parking available behind the building for $95/mo (but in the meantime, street parking is easily found for a city parking sticker of $60/year). There's not many other units available in Evanston for a 5/1 start lease, so I might not do too much more apartment hunting.